Search results for: Taylor’s Series Method

Authors: Yuzuru Mitsui, Takashi Ikegami

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The exponents of Taylor’s law in deterministic chaotic systems are computed, and their meanings are intensively discussed. Taylor’s law is the scaling relationship between the mean and variance (in both space and time) of population abundance, and this law is known to hold in a variety of ecological time series. The exponents found in the temporal Taylor’s law are different from those of the spatial Taylor’s law. The temporal Taylor’s law is calculated on the time series from the same locations (or the same initial states) of different temporal phases. However, with the spatial Taylor’s law, the mean and variance are calculated from the same temporal phase sampled from different places. Most previous studies were done with stochastic models, but we computed the temporal and spatial Taylor’s law in deterministic systems. The temporal Taylor’s law evaluated using the same initial state, and the spatial Taylor’s law was evaluated using the ensemble average and variance. There were two main discoveries from this work. First, it is often stated that deterministic systems tend to have the value two for Taylor’s exponent. However, most of the calculated exponents here were not two. Second, we investigated the relationships between chaotic features measured by the Lyapunov exponent, the correlation dimension, and other indexes with Taylor’s exponents. No strong correlations were found; however, there is some relationship in the same model, but with different parameter values, and we will discuss the meaning of those results at the end of this paper.

Keywords: chaos, density effect, population dynamics, Taylor’s law

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: F. J. Adeyeye, D. Eni, K. M. Okedoye

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In this paper we present a Hybrid of Adomian decomposition method (ADM). This is the substitution of a One-step method of Taylor’s series approximation of orders I and II, into the nonlinear part of Adomian decomposition method resulting in a convergent series scheme. This scheme is applied to solve some Logistic problems represented as Abelian differential equation and the results are compared with the actual solution and Runge-kutta of order IV in order to ascertain the accuracy and efficiency of the scheme. The findings shows that the scheme is efficient enough to solve logistic problems considered in this paper.

Keywords: Adomian decomposition method, nonlinear part, one-step method, Taylor series approximation, hybrid of Adomian polynomial, logistic problem, Malthusian parameter, Verhulst Model

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Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

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Authors: L. Q. Yuan, J. Yang, A. Siddiqui

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A new regression uncertainty analysis methodology was applied to determine the uncertainties of the critical heat flux (CHF) power correlation for an advanced 43-element bundle design, which was developed by Canadian Nuclear Laboratories (CNL) to achieve improved economics, resource utilization and energy sustainability. The new methodology is considered more appropriate than the traditional methodology in the assessment of the experimental uncertainty associated with regressions. The methodology was first assessed using both the Monte Carlo Method (MCM) and the Taylor Series Method (TSM) for a simple linear regression model, and then extended successfully to a non-linear CHF power regression model (CHF power as a function of inlet temperature, outlet pressure and mass flow rate). The regression uncertainty assessed by MCM agrees well with that by TSM. An equation to evaluate the CHF power regression uncertainty was developed and expressed as a function of independent variables that determine the CHF power.

Keywords: CHF experiment, CHF correlation, regression uncertainty, Monte Carlo Method, Taylor Series Method

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Authors: Ahmed M. Mansour, Ali M. El-Sawy, Ahmed T. Sayed

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Logarithms reduce products to sums and powers to products; they play an important role in signal processing, communication and information theory. They are primarily used for hardware calculations, handling multiplications, divisions, powers, and roots effectively. There are three commonly used bases for logarithms; the logarithm with base-10 is called the common logarithm, the natural logarithm with base-e and the binary logarithm with base-2. This paper demonstrates different methods of calculation for log2 showing the complexity of each and finds out the most accurate and efficient besides giving in- sights to their hardware design. We present a new method called Floor Shift for fast calculation of log2, and then we combine this algorithm with Taylor series to improve the accuracy of the output, we illustrate that by using two examples. We finally compare the algorithms and conclude with our remarks.

Keywords: logarithms, log2, floor, iterative, CORDIC, Taylor series

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Authors: Ahmed Esmael, Ali El Shrif

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In this study the instability problem of a modified Taylor-Couette flow between two vertical coaxial cylinders of radius R1, R2 is considered. The modification is based on the wavy shape of the inner cylinder surface, where inner cylinders with different surface amplitude and wavelength are used. The study aims to discover the effect of the inner surface geometry on the instability phenomenon that undergoes Taylor-Couette flow. The study reveals that the transition processes depends strongly on the amplitude and wavelength of the inner cylinder surface and resulting in flow instabilities that are strongly different from that encountered in the case of the classical Taylor-Couette flow.

Keywords: hydrodynamic instability, Modified Taylor-Couette Flow, turbulence, Taylor vortices

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Authors: Baya Takhedmit, Karim Abbas, Sofiane Ouazine

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The vacations queues are often employed to model many real situations such as computer systems, communication networks, manufacturing and production systems, transportation systems and so forth. These queueing models are solved at fixed parameters values. However, the parameter values themselves are determined from a finite number of observations and hence have uncertainty associated with them (epistemic uncertainty). In this paper, we consider the M/G/1/N queue with server vacation and exhaustive discipline where we assume that the vacation parameter values have uncertainty. We use the Taylor series expansions approach to estimate the expectation and variance of model output, due to epistemic uncertainties in the model input parameters.

Keywords: epistemic uncertainty, M/G/1/N queue with vacations, non-parametric sensitivity analysis, Taylor series expansion

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Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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Authors: Yosra Baaziz, Moez Labidi

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Given limited research on monetary policy rules in revolutionary countries, this paper challenges the suitability of the Taylor rule in characterizing the monetary policy behavior of the Tunisian Central Bank (BCT), especially in turbulent times. More specifically, we investigate the possibility that the Taylor rule should be formulated as a threshold process and examine the validity of such nonlinear Taylor rule as a robust rule for conducting monetary policy in Tunisia. Using quarterly data from 1998:Q4 to 2013:Q4 to analyze the movement of nominal short-term interest rate of the BCT, we find that the nonlinear Taylor rule improves its performance with the advent of special events providing thus a better description of the Tunisian interest rate setting. In particular, our results show that the adoption of an appropriate nonlinear approach leads to a reduction in the errors of 150 basis points in 1999 and 2009, and 60 basis points in 2011, relative to the linear approach.

Keywords: policy rule, central bank, exchange rate, taylor rule, nonlinearity

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Reza Moosavi Mohseni, Wenjun Zhang, Jiling Cao

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The aim of the present study is to detect the chaotic behavior in monetary economic relevant dynamical system. The study employs three different forms of Taylor rules: current, forward, and backward looking. The result suggests the existence of the chaotic behavior in all three systems. In addition, the results strongly represent that using expectations especially rational expectation hypothesis can increase complexity of the system and leads to more chaotic behavior.

Keywords: taylor rule, monetary system, chaos theory, lyapunov exponent, GMM estimator

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Authors: K. Godazandeh, K. Sadeghy

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In the present study, the effect of magnetic field on the hydrodynamic instability of Taylor-Couette flow between two concentric rotating cylinders has been numerically investigated. At the beginning the basic flow has been solved using continuity, Cauchy equations (with regards to Lorentz force) and the constitutive equations of a viscoelastic model called "Giesekus" model. Small perturbations, considered to be normal mode, have been superimposed to the basic flow and the unsteady perturbation equations have been derived consequently. Neglecting non-linear terms, the general eigenvalue problem obtained has been solved using pseudo spectral method (combination of Chebyshev polynomials). The objective of the calculations is to study the effect of magnetic fields on the onset of first mode of instability (axisymmetric mode) for different dimensionless parameters of the flow. The results show that the stability picture is highly influenced by the magnetic field. When magnetic field increases, it first has a destabilization effect which changes to stabilization effect due to more increase of magnetic fields. Therefor there is a critical magnetic number (Hartmann number) for instability of Taylor-Couette flow. Also, the effect of magnetic field is more dominant in large gaps. Also based on the results obtained, magnetic field shows a more considerable effect on the stability at higher Weissenberg numbers (at higher elasticity), while the "mobility factor" changes show no dominant role on the intense of suction and injection effect on the flow's instability.

Keywords: magnetic field, Taylor-Couette flow, Giesekus model, pseudo spectral method, Chebyshev polynomials, Hartmann number, Weissenberg number, mobility factor

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Authors: K. Noah, F.-S. Lien

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In Computational Fluid Dynamics (CFD), there are a variety of numerical methods, of which some depend on macroscopic model representatives. These models can be solved by finite-volume, finite-element or finite-difference methods on a microscopic description. However, the lattice Boltzmann method (LBM) is considered to be a mesoscopic particle method, with its scale lying between the macroscopic and microscopic scales. The LBM works well for solving incompressible flow problems, but certain limitations arise from solving compressible flows, particularly at high Mach numbers. An improved lattice Boltzmann model for compressible flow problems is presented in this research study. A higher-order Taylor series expansion of the Maxwell equilibrium distribution function is used to overcome limitations in LBM when solving high-Mach-number flows. Large eddy simulation (LES) is implemented in LBM to simulate turbulent jet flows. The results have been validated with available experimental data for turbulent compressible free jet flow at subsonic speeds.

Keywords: compressible lattice Boltzmann method, multiple relaxation times, large eddy simulation, turbulent jet flows

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Authors: Plessen Mogens Graf

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Within the context of multivariate time series segmentation, this paper proposes a method inspired by a posteriori optimal trading. After a normalization step, time series are treated channelwise as surrogate stock prices that can be traded optimally a posteriori in a virtual portfolio holding either stock or cash. Linear transaction costs are interpreted as hyperparameters for noise filtering. Trading signals, as well as trading signals obtained on the reversed time series, are used for unsupervised channelwise labeling before a consensus over all channels is reached that determines the final segmentation time instants. The method is model-free such that no model prescriptions for segments are made. Benefits of proposed approach include simplicity, computational efficiency, and adaptability to a wide range of different shapes of time series. Performance is demonstrated on synthetic and real-world data, including a large-scale dataset comprising a multivariate time series of dimension 1000 and length 2709. Proposed method is compared to a popular model-based bottom-up approach fitting piecewise affine models and to a recent model-based top-down approach fitting Gaussian models and found to be consistently faster while producing more intuitive results in the sense of segmenting time series at peaks and valleys.

Keywords: time series segmentation, model-free, trading-inspired, multivariate data

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Mohamed Seghouani, Ahmed Tafraoui, Soltane Lebaili

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The purpose of this study widened knowledge on the use of the cutting tools out of metal carbide and to define it the influence of the elements of the mode of cut on the behavior of these tools during the machining of treated steel XC38 and untreated. This work aims at evolution determined in experiments of the wear of a cutting tool out of metal carbide with plate reported of P30 nuance for an operation of slide-lathing in turning on soaked and not hardened steel XC38 test-tubes. This research is based on the model of Taylor to determine the life span of the cutting tool according to the various parameters of cut, like the cutting speed Vc, the advance of cut a, the depth of cutting P. In order to express the operational limits of the tool for slide-lathing in a preventive way. The model makes it possible to determine the time of change of the tool and to regard it as a constraint for the respect of the roughness of the workpiece during a work of series in conventional machining.

Keywords: machining, wear, lifespan, model of Taylor, cutting tool, carburize metal

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Authors: Mohammadreza Akbari, Sara Akbari, Davood Domiri Ganji, Pooya Solimani, Reza Khalili

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In this paper, three complicated nonlinear differential equations(PDE,ODE) in the field of engineering and non-vibration have been analyzed and solved completely by new method that we have named it Akbari-Ganji's Method (AGM) . As regards the previous published papers, investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by Numerical Method. Based on the comparisons which have been made between the gained solutions by AGM and Numerical Method (Runge-Kutta 4th), it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. Furthermore, It is necessary to mention that a summary of the excellence of this method in comparison with the other approaches can be considered as follows: It is noteworthy that these results have been indicated that this approach is very effective and easy therefore it can be applied for other kinds of nonlinear equations, And also the reasons of selecting the mentioned method for solving differential equations in a wide variety of fields not only in vibrations but also in different fields of sciences such as fluid mechanics, solid mechanics, chemical engineering, etc. Therefore, a solution with high precision will be acquired. With regard to the afore-mentioned explanations, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods. And also one of the important position that is explored in this paper is: Trigonometric and exponential terms in the differential equation (the method AGM) , is no need to use Taylor series Expansion to enhance the precision of the result.

Keywords: new method (AGM), complex non-linear partial differential equations, damping ratio, energy lost per cycle

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Authors: Balachandra Kumaraswamy, P. G. Poonacha

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Automatic Music Information Retrieval has been one of the challenging topics of research for a few decades now with several interesting approaches reported in the literature. In this paper we have developed a pitch extraction method based on a finite Fourier series approximation to the given window of samples. We then estimate pitch as the fundamental period of the finite Fourier series approximation to the given window of samples. This method uses analysis of the strength of harmonics present in the signal to reduce octave as well as harmonic errors. The performance of our method is compared with three best known methods for pitch extraction, namely, Yin, Windowed Special Normalization of the Auto-Correlation Function and Harmonic Product Spectrum methods of pitch extraction. Our study with artificially created signals as well as music files show that Fourier Approximation method gives much better estimate of pitch with less octave and harmonic errors.

Keywords: pitch, fourier series, yin, normalization of the auto- correlation function, harmonic product, mean square error

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Mohammad H. Fattahi

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Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. The noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: chaotic behavior, wavelet, noise reduction, river flow

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Authors: Chetsada Noknoi

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The acceptance of Y series refers to the willingness and enjoyment of watching Y series without feeling different from general series. This occurs when people watch Y series and derive happiness and entertainment from it. The viewing experience has the most significant impact on Y series acceptance. This research aims to 1) investigate the levels of acceptance of sexual diversity, image of Y series Actors, media exposure, and Y series acceptance among the residents in three southern border provinces of Thailand, and 2) examine how acceptance of sexual diversity, actor perceptions in Y series, and media exposure influence Y series acceptance in these provinces. The sample consisted of 322 participants from the three southern border provinces of Thailand. The research instrument used was a questionnaire, and data were analyzed using frequency, percentage, mean, standard deviation, and multiple regression analysis. The findings revealed that overall, acceptance of sexual diversity, Image of Y series Actors, and Y series acceptance among the residents in three southern border provinces of Thailand were at a high level, while media exposure was moderate overall. However, the two factors that had the most significant impact on Y series acceptance in these provinces, ranked from highest to lowest influence, were media exposure and acceptance of sexual diversity. Both of these factors had a positive effect on Y series acceptance among the residents in three southern border provinces of Thailand. Collectively, these factors accounted for 40.7% of the variance in Y series acceptance among the residents in three southern border provinces of Thailand.

Keywords: acceptance, acceptance of sexual diversity, image of Y series actors, media exposure, Y series

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Authors: Siriporn Meenanan

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The objective of this study is to investigate the attitude of Thai students towards the Thai series "Hormones the Series Season 2". This study was conducted in the quantitative research, and the questionnaires were used to collect data from 400 people of the sample group. Descriptive statistics were used in data analysis. The findings reveal that most participants have positive comments regarding the series. They strongly agreed that the series reflects on the way of life and problems of teenagers in Thailand. Hence, the participants believe that if adults have a chance to watch the series, they will have the better understanding of the teenagers. In addition, the participants also agreed that the contents of the play are appropriate and satisfiable as the contents of “Hormones the Series Season 2” will raise awareness among the teens and use it as a guide to prevent problems that might happen during their teenage life.

Keywords: content analysis, attitude, Thai series, hormones the Series

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi, Aref Ghafouri

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Recent research in neural networks science and neuroscience for modeling complex time series data and statistical learning has focused mostly on learning from high input space and signals. Local linear models are a strong choice for modeling local nonlinearity in data series. Locally weighted projection regression is a flexible and powerful algorithm for nonlinear approximation in high dimensional signal spaces. In this paper, different learning scenario of one and two dimensional data series with different distributions are investigated for simulation and further noise is inputted to data distribution for making different disordered distribution in time series data and for evaluation of algorithm in locality prediction of nonlinearity. Then, the performance of this algorithm is simulated and also when the distribution of data is high or when the number of data is less the sensitivity of this approach to data distribution and influence of important parameter of local validity in this algorithm with different data distribution is explained.

Keywords: local nonlinear estimation, LWPR algorithm, online training method, locally weighted projection regression method

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Authors: Ibetombi Soibam

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Li-Zn-Ni ferrite having the compositional formula Li0.4-0.5xZn0.2NixFe2.4-0.5xO4 where x = 0.02 ≤ x ≤0.1 in steps of 0.02 was fabricated by the citrate precursor method. In this method, metal nitrates and citric acid was used to prepare the gel which exhibit self-propagating combustion behavior giving the required ferrite sample. The ferrite sample was given a pre-firing at 650°C in a programmable conventional furnace for 3 hours with a heating rate of 5°C/min. A series of the sample was finally given conventional sintering (CS) at 1040°C after the pre-firing process. Another series was given microwave sintering (MS) at 1040°C in a programmable microwave furnace which uses a single magnetron operating at 2.45 GHz frequency. X- ray diffraction pattern confirmed the spinel phase structure for both the series. The theoretical and experimental density was calculated. It was observed that densification increases with the increase in Ni concentration in both the series. However, samples sintered by microwave technique was found to be denser. The microstructure of the two series of the sample was examined using scanning electron microscopy (SEM). Dielectric properties have been investigated as a function of frequency and composition for both series of samples sintered by CS and MS technique. The variation of dielectric constant with frequency show dispersion for both the series. It was explained in terms of Koop’s two layer model. From the analysis of dielectric measurement, it was observed that the value of room temperature dielectric constant decreases with the increase in Ni concentration for both the series. The microwave sintered samples show a lower dielectric constant making microwave sintering suitable for high-frequency applications. The possible mechanisms contributing to all the above behavior is being discussed.

Keywords: citrate precursor, dielectric constant, ferrites, microwave sintering

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Authors: Kunya Bowornchockchai

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The objective of this research is to forecast the monthly exchange rate between Thai baht and the US dollar and to compare two forecasting methods. The methods are Box-Jenkins’ method and Holt’s method. Results show that the Box-Jenkins’ method is the most suitable method for the monthly Exchange Rate between Thai Baht and the US Dollar. The suitable forecasting model is ARIMA (1,1,0)  without constant and the forecasting equation is Y_t = Y_t-1 + 0.3691 (Y_t-1 - Y_t-2) When Y_t  is the time series data at time t, respectively.

Keywords: Box–Jenkins method, Holt’s method, mean absolute percentage error (MAPE), exchange rate

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Authors: A. K. M. Kamrul Islam, Abdelhamid Bouchachia, Suang Cang, Hongnian Yu

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Forecasting model has a great impact in terms of prediction and continues to do so into the future. Although many forecasting models have been studied in recent years, most researchers focus on different forecasting methods based on fuzzy time series to solve forecasting problems. The forecasted models accuracy fully depends on the two terms that are the length of the interval in the universe of discourse and the content of the forecast rules. Moreover, a hybrid forecasting method can be an effective and efficient way to improve forecasts rather than an individual forecasting model. There are different hybrids forecasting models which combined fuzzy time series with evolutionary algorithms, but the performances are not quite satisfactory. In this paper, we proposed a hybrid forecasting model which deals with the first order as well as high order fuzzy time series and particle swarm optimization to improve the forecasted accuracy. The proposed method used the historical enrollments of the University of Alabama as dataset in the forecasting process. Firstly, we considered an automatic clustering algorithm to calculate the appropriate interval for the historical enrollments. Then particle swarm optimization and fuzzy time series are combined that shows better forecasting accuracy than other existing forecasting models.

Keywords: fuzzy time series (fts), particle swarm optimization, clustering algorithm, hybrid forecasting model

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Authors: Hisyam Hidayatullah

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This world events consciously or not realize everything has a pattern, until the events of the universe according to the Big Bang theory of the solar system which makes so regular in the rotation. The author would like to create a results curve area between the quadratic function y=kx2 and line y=ka2 using GeoGebra application version 4.2. This paper can provide a series that is no less interesting with Fourier series, so that will add new material about the series can be calculated with sigma notation. In addition, the ranks of the unique natural numbers of extensive changes in established areas. Finally, this paper provides analytical and geometric proof of the vast area in between the lines and curves that give the area is formed by y=ka2 dan kurva y=kx2, x-axis, line x=√a and x=-√a make a series of numbers for k=1 and a ∈ original numbers. ∑_(i=0)^n=(4n√n)/3=0+4/3+(8√2)/3+4√3+⋯+(4n√n)/3. The author calls the series “H154M”.

Keywords: sequence, series, sigma notation, application GeoGebra

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Authors: Terigele

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Cultural products are always shelved into different classes of a hierarchy that separates so-called highbrow and lowbrow cultures. This study illustrated that audiences might even construct a hierarchy according to the origin countries when consuming certain products. Chinese audiences now have access to TV series from all around the world thanks to the internet. TV series from different origin countries show some particular features in terms of length, theme, plots, accessibility, seriousness etc. Their audiences were therefore stereotyped because of what they watch. Based on in-depth interviews with 20 participants, this research has following findings: 1) Most popular origin countries of foreign TV series in China are Korea, the United States, the United Kingdom, Japan and European countries in a descending order. Korean TV series are most popular because they are less serious and more accessible compared to others. 2) In the hierarchy of the TV series, European TV series stand on the top followed by British and American TV series. Japanese TV series are also categorized into highbrow class. Korean TV series are at the bottom and always seen as lowbrow cultural products. 3) Most audiences consume TV series from more than one origin countries and have different needs when watching them. Participants reported that they watch European TV series because those TV series are more artistic than their counterparts and of great quality. They watch British and American TV series mainly to improve their English and to learn about the culture. They find Japanese TV series very enjoyable with a large variety of themes and impressive lines. Audiences watch Korean TV series mostly to entertain and kill time. 4) Audiences do care about cultural taste. Especially those who watch European, British and American TV series usually tend to consider audiences who watch nothing but Korean TV series to be shallow. On the other hand, Korean TV series’ audiences seem to care less about the hierarchy of the TV series. Even when they discuss the hierarchy, they tend to accept the judgments with ironies and jokes. Future studies can dig deeply into the genre and content of TV series with different origin countries and also investigate more about the psychology of audiences regarding the gender, age, education, socioeconomic status etc.

Keywords: foreign TV series, hierarchy, popularity, uses and gratification

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